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Simplifying 5x2 + -16x + -6384 = 0 Reorder the terms: -6384 + -16x + 5x2 = 0 Solving -6384 + -16x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1276.8 + -3.2x + x2 = 0 Move the constant term to the right: Add '1276.8' to each side of the equation. -1276.8 + -3.2x + 1276.8 + x2 = 0 + 1276.8 Reorder the terms: -1276.8 + 1276.8 + -3.2x + x2 = 0 + 1276.8 Combine like terms: -1276.8 + 1276.8 = 0.0 0.0 + -3.2x + x2 = 0 + 1276.8 -3.2x + x2 = 0 + 1276.8 Combine like terms: 0 + 1276.8 = 1276.8 -3.2x + x2 = 1276.8 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 1276.8 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 1276.8 + 2.56 Combine like terms: 1276.8 + 2.56 = 1279.36 2.56 + -3.2x + x2 = 1279.36 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 1279.36 Calculate the square root of the right side: 35.76814225 Break this problem into two subproblems by setting (x + -1.6) equal to 35.76814225 and -35.76814225.Subproblem 1
x + -1.6 = 35.76814225 Simplifying x + -1.6 = 35.76814225 Reorder the terms: -1.6 + x = 35.76814225 Solving -1.6 + x = 35.76814225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 35.76814225 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 35.76814225 + 1.6 x = 35.76814225 + 1.6 Combine like terms: 35.76814225 + 1.6 = 37.36814225 x = 37.36814225 Simplifying x = 37.36814225Subproblem 2
x + -1.6 = -35.76814225 Simplifying x + -1.6 = -35.76814225 Reorder the terms: -1.6 + x = -35.76814225 Solving -1.6 + x = -35.76814225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -35.76814225 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -35.76814225 + 1.6 x = -35.76814225 + 1.6 Combine like terms: -35.76814225 + 1.6 = -34.16814225 x = -34.16814225 Simplifying x = -34.16814225Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.36814225, -34.16814225}
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